Chapter 3 Valuing Bonds 51
bre44380_ch03_046-075.indd 51 09/30/15 12:47 PM
◗ FIGURE 3.2
Plot of bond prices as a function
of the interest rate. The price of
long-term bonds is more sensitive to
changes in the interest rate than is the
price of short-term bonds.0500100015002000250030-year bond3-year bond02143658719 0
Interest rate, %Bond price, dollarsWhen the interest rate
equals the 4.25% coupon,
both bonds sell for
face valueAs interest rates change, so do bond prices. For example, suppose that investors demanded
a semiannual return of 4% on the 4.25s of 2017, rather than the .4825% semiannual return we
used previously. In that case the price would be
PV = _____ 21.25
1.04+ _____ 21.25
1.04^2+ _____ 21.25
1.04^3+ _____ 21.25
1.04^4+ _____21.25
1.04^5+ ________ 1,021.25
1.04^6= $901.71The higher interest rate results in a lower price.
Bond prices and interest rates must move in opposite directions. The yield to maturity, our
measure of the interest rate on a bond, is defined as the discount rate that explains the bond
price. When bond prices fall, interest rates (that is, yields to maturity) must rise. When inter-
est rates rise, bond prices must fall. We recall a hapless TV pundit who intoned, “The recent
decline in long-term interest rates suggests that long-term bond prices may rise over the next
week or two.” Of course the bond prices had already gone up. We are confident that you won’t
make the pundit’s mistake.
The solid dark red line in Figure 3.2 shows the value of our 4.25% bond for different inter-
est rates. As the yield to maturity falls, the bond price increases. When the annual yield is
equal to the bond’s annual coupon rate (4.25%), the bond sells for exactly its face value. When
the yield is higher than 4.25%, the bond sells at a discount to face value. When the yield is
lower than 4.25%, the bond sells at a premium.
Bond investors cross their fingers that market interest rates will fall, so that the price of
their securities will rise. If they are unlucky and interest rates jump up, the value of their
investment declines.
On May 15, 2008, the U.S. Treasury sold $9 billion of 4.375% bonds maturing in February
- The bonds were issued at a price of 96.38% and offered a yield to maturity of 4.60%.
This was the return to anyone buying at the issue price and holding the bonds to maturity. In
EXAMPLE 3.1^ ●^ Changes in Interest Rates and Bond Returns